Experimentally injecting and measureing the tracer in a laminar flow reactor can be a difficult task, if not a nightmare. For example, if one uses tracer chemicals that are photo-activated as they enter the reactor, the analysis and interpretation of E(t) from the data becomes much more involved.

Diagnostics and Troubleshooting

The CSTR

Concentration

RTD Function

Cumulative Function

Space Time

a. Perfect Operation

b. Passing (BP)

c. Dead Volume

A summary for ideal CSTR mixing volume is shown in Figure 13-14

Tubular Reactor

A similar analysis to that for a CSTR can be carried out on a tubular reactor.

a. Perfect Operation of PFR (P)

b. PFR with Channeling (Bypassing, BP)

c. PFR with Dead Volume (DV)

A summary for PRF is shown in Figure 13-18

In addition to its use in diagnosis, the RTD can be used to predict conversion in existing reactors when a new reaction is tried in an old reactor. However, the RTD is not unique for a given system, and we need to develop models for the RTD to predict conversion.

If using mathematical software to apply the models described below, you may need to fit C(t) and E(t) to a polynomial. The procedure for fitting C(t) and E(t) to a polynomial is identical to the techniques use to fitting concentration as a function of time described in Chapter 5.

Polymath regression analysis tutorial

Use combinations of ideal reactors to model real reactors that could also include:
Zero parameter models

Segregation Model

Maximum Mixedness Model

One parameter models

Tanks-in-Series Model

Dispersion Model

Two parameter models

Bypassing

Dead Space

Recycle

4A. Segregation Model

Models the real reactor as a number of small batch reactors, each spending a different
time in the reactor. All molecules that spend the same length of
time in the reactor (i.e., that are of the same age) remain together in
the same globule (i.e., batch reactor). Mixing of the different age groups
occurs at the last possible moment at the reactor exit.

Mixing of the
globules of different ages occurs here.

Little batch reactors (globules) inside a CSTR.

X3>X2>X1

Mixing occurs at the latest possible moment.Each little batch reactor (globule) exiting the real reactor at different
times will have a different conversion. (X1,X2,X3...)

For multiple reactions use an ODE solver to couple the mole balance equations, dCi/dt=ri,
with the segregation model equations: d/dt=Ci(t)*E(t), where C
i is the concentration of i in the batch reactor at time t andis the concentration of i after mixing the batch reactors at the exit.

Batch, PFR, CSTR, Segregation

4B Maximum Mixedness Model

Mixing occurs at the earliest possible moment.

Note E(l)=E(t)

E(l)dl =Fraction
of molecules that have a life expectancy between l+dl
and l.

Modeling maximum mixedness as a plug flow reactor with side entrances.

Dividing byDland taking the limit asDlgoes to zero. Substitute,

Differentiating
the first term and recalling we obtain.

We need to integrate backwards from(the entrance) to= 0
(the exit). In real systems we have some maximum value of(say= 200 minutes) rather thanminutes. Consequently we integrate backward from= 200. However, because most ODE packages will not integrate backwards, we have to use the transfer

For multiple reactions use an ODE solver to couple the mole balance equations, dCi/dt=ri
(where ri is the net rate of reaction),
with the segregation model equations: dCi/dt=Ci(t)*E(t)
as previously shown. For maximum mixedness:

To obtain solutions with an ODE solver, first fit E(t) to a polynomial
or several polynomials. Then let
z = T -where T is the largest time in which E(t) is recorded. Proceed to solve
the resulting equations.

Object Assessment of Chapter 13

*
All chapter references are for the 4th Edition of the text Elements of Chemical Reaction Engineering
.